Diderot on Nicholas Saunderson

Diderot wrote Letter on the Blind in which he attempted to answer a question that had been posed by philosophers. Suppose a blind man recovered his sight and was shown a cube and a sphere. Would be able to correctly name them? In the quotation below, taken from M J Morgan, Molyneux's question (Oxford University Press, Oxford, 1977), Diderot discusses Nicholas Saunderson:

This Saunderson, Madame, is another blind person whom it would not be irrelevant to consider here. Wondrous things are told about him, and his progress in literature and in the mathematical sciences lends credence to all of them.

He was the author of a very perfect book of its kind, the Elements of Algebra, in which the only clue to his blindness is the occasional eccentricity of his demonstrations, which would perhaps not have been thought up by a sighted person. To him belongs the division of the cube into six equal pyramids having their vertices at the centre of the cube and the six faces as their bases; this is used for an elegant proof that a pyramid is one-third of a prism having the same base and height.

Saunderson taught mathematics at the University of Cambridge with astonishing success. He gave lessons in optics, and on the nature of light and colours; he explained the theory of vision; he considered the effects of lenses, the rainbow and many other matters relating to sight and the eye. These facts lose much of their strangeness, Madame, if you consider that there are three things which must be distinguished in any question that combines geometrical and physical considerations: the phenomena to be explained; the axioms of the geometry; and the calculation which follows from the axiom. Now, it is obvious that however acute the blind man may be, the phenomena of light and colour are completely unknown to him. He will understand the axioms, because he refers them to palpable objects, but he will not understand why geometry should prefer them to other axioms, for to do so he would have to compare the axioms with the phenomena directly, which for him is an impossibility. The blind man thus takes the axioms as they are given to him; he interprets a ray of light as a thin elastic thread, or as a succession of tiny bodies that strike the eyes with incredible force - and he calculates accordingly. The boundary between physics and mathematics has been crossed, and the problem becomes purely formal.

JOC/EFR December 2008

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